Associated manuscript: INSERT

Section 1. Simulation: Calibration curves of product method

These are the same plot type as Figure 2 in the manuscript, plotted for every sample size

## Loading required package: ggplot2

Figure S1.1: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S1.2: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S1.3: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 5000)

Section 2. Simulation: Median calibration curve across the 1000 simulation iterations (average calibration) for each data generating mechanism, scenario and sample size

Figure S2.1: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.2: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.3: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.4: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.5: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.6: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.7: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.8: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.9: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.10: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.11: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.12: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 5000)

Section 3. Simulation: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for each data generating mechanism, scenario and sample size

Figure S3.1: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.2: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.3: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.4: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.5: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.6: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.7: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.8: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.9: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.10: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.11: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.12: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 5000)

Section 4. Simulation: Discrimination tables

Table S4.1: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.79 (0.061) 0.785 (0.063) 0.782 (0.065) 0.79 (0.061) 0.79 (0.062) 0.79 (0.061) 0.79 (0.061) 0.79 (0.061)
DGM2 (c-clay) 0.788 (0.06) 0.781 (0.064) 0.778 (0.067) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06)
DGM3 (c-gumb) 0.757 (0.065) 0.749 (0.068) 0.746 (0.071) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065)
DGM4 (c-frank) 0.779 (0.061) 0.773 (0.064) 0.771 (0.065) 0.779 (0.061) 0.779 (0.061) 0.779 (0.062) 0.779 (0.061) 0.779 (0.061)
DGM5 (f-norm) 0.779 (0.063) 0.773 (0.065) 0.77 (0.067) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063)
DGM6 (f-gam) 0.78 (0.06) 0.774 (0.064) 0.771 (0.064) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06)

Table S4.2: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.791 (0.064) 0.788 (0.065) 0.788 (0.065) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064)
DGM2 (c-clay) 0.786 (0.062) 0.784 (0.062) 0.783 (0.063) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062)
DGM3 (c-gumb) 0.758 (0.064) 0.756 (0.065) 0.756 (0.065) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064)
DGM4 (c-frank) 0.78 (0.062) 0.777 (0.063) 0.777 (0.063) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062)
DGM5 (f-norm) 0.778 (0.061) 0.776 (0.061) 0.776 (0.061) 0.778 (0.061) 0.777 (0.061) 0.778 (0.061) 0.777 (0.061) 0.777 (0.061)
DGM6 (f-gam) 0.787 (0.06) 0.784 (0.06) 0.784 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06)

Table S4.3: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.791 (0.06) 0.79 (0.06) 0.79 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06)
DGM2 (c-clay) 0.783 (0.061) 0.782 (0.062) 0.782 (0.062) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061)
DGM3 (c-gumb) 0.759 (0.062) 0.758 (0.063) 0.757 (0.063) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062)
DGM4 (c-frank) 0.777 (0.063) 0.777 (0.062) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063)
DGM5 (f-norm) 0.78 (0.061) 0.779 (0.061) 0.779 (0.062) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061)
DGM6 (f-gam) 0.781 (0.061) 0.78 (0.061) 0.78 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061)

Table S4.4: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.785 (0.054) 0.781 (0.056) 0.779 (0.057) 0.785 (0.054) 0.784 (0.055) 0.785 (0.054) 0.784 (0.054) 0.784 (0.054)
DGM2 (c-clay) 0.783 (0.054) 0.778 (0.056) 0.775 (0.057) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054)
DGM3 (c-gumb) 0.733 (0.063) 0.726 (0.066) 0.723 (0.067) 0.733 (0.063) 0.733 (0.063) 0.733 (0.063) 0.732 (0.063) 0.732 (0.063)
DGM4 (c-frank) 0.772 (0.056) 0.767 (0.058) 0.766 (0.059) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056)
DGM5 (f-norm) 0.763 (0.057) 0.757 (0.059) 0.756 (0.059) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057)
DGM6 (f-gam) 0.766 (0.056) 0.761 (0.06) 0.76 (0.06) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056)

Table S4.5: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.785 (0.055) 0.783 (0.055) 0.783 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055)
DGM2 (c-clay) 0.781 (0.056) 0.779 (0.056) 0.779 (0.057) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056)
DGM3 (c-gumb) 0.737 (0.061) 0.735 (0.062) 0.735 (0.062) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061)
DGM4 (c-frank) 0.773 (0.057) 0.771 (0.057) 0.771 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057)
DGM5 (f-norm) 0.763 (0.057) 0.761 (0.057) 0.761 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057)
DGM6 (f-gam) 0.77 (0.056) 0.768 (0.056) 0.768 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056)

Table S4.6: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.788 (0.054) 0.787 (0.054) 0.787 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054)
DGM2 (c-clay) 0.777 (0.056) 0.776 (0.056) 0.776 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056)
DGM3 (c-gumb) 0.735 (0.059) 0.734 (0.059) 0.734 (0.06) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059)
DGM4 (c-frank) 0.77 (0.055) 0.77 (0.054) 0.77 (0.054) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055)
DGM5 (f-norm) 0.764 (0.056) 0.763 (0.056) 0.763 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056)
DGM6 (f-gam) 0.769 (0.058) 0.767 (0.058) 0.767 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058)

Table S4.7: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.019) 0.794 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019)
DGM3 (c-gumb) 0.766 (0.021) 0.765 (0.021) 0.765 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021)
DGM4 (c-frank) 0.786 (0.018) 0.785 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018)
DGM5 (f-norm) 0.779 (0.02) 0.778 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02)
DGM6 (f-gam) 0.788 (0.019) 0.787 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02)

Table S4.8: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019)
DGM3 (c-gumb) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.767 (0.021) 0.767 (0.021) 0.767 (0.021) 0.767 (0.021)
DGM4 (c-frank) 0.786 (0.019) 0.785 (0.02) 0.786 (0.02) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019)
DGM5 (f-norm) 0.78 (0.019) 0.779 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019)
DGM6 (f-gam) 0.789 (0.019) 0.788 (0.019) 0.788 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019)

Table S4.9: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018)
DGM3 (c-gumb) 0.766 (0.02) 0.765 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02)
DGM4 (c-frank) 0.785 (0.02) 0.784 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02)
DGM5 (f-norm) 0.779 (0.019) 0.778 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019)
DGM6 (f-gam) 0.79 (0.018) 0.789 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018)

Table S4.10: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.776 (0.018) 0.776 (0.018) 0.776 (0.017) 0.776 (0.017) 0.776 (0.018) 0.776 (0.017) 0.776 (0.017) 0.776 (0.017)
DGM2 (c-clay) 0.774 (0.018) 0.773 (0.018) 0.774 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018)
DGM3 (c-gumb) 0.731 (0.02) 0.73 (0.02) 0.73 (0.02) 0.731 (0.02) 0.732 (0.02) 0.732 (0.02) 0.732 (0.02) 0.732 (0.02)
DGM4 (c-frank) 0.761 (0.017) 0.759 (0.017) 0.761 (0.017) 0.761 (0.021) 0.761 (0.017) 0.761 (0.017) 0.761 (0.017) 0.761 (0.017)
DGM5 (f-norm) 0.747 (0.019) 0.746 (0.019) 0.746 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019)
DGM6 (f-gam) 0.77 (0.018) 0.769 (0.018) 0.77 (0.018) 0.77 (0.018) 0.77 (0.017) 0.77 (0.018) 0.771 (0.018) 0.771 (0.018)

Table S4.11: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018)
DGM2 (c-clay) 0.774 (0.018) 0.773 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018)
DGM3 (c-gumb) 0.732 (0.02) 0.731 (0.02) 0.732 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02)
DGM4 (c-frank) 0.76 (0.019) 0.759 (0.019) 0.76 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019)
DGM5 (f-norm) 0.747 (0.018) 0.746 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.019) 0.747 (0.019)
DGM6 (f-gam) 0.771 (0.017) 0.77 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017)

Table S4.12: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.778 (0.018) 0.777 (0.018) 0.778 (0.018) 0.778 (0.018) 0.778 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018)
DGM2 (c-clay) 0.773 (0.017) 0.772 (0.018) 0.773 (0.017) 0.774 (0.017) 0.773 (0.017) 0.774 (0.017) 0.774 (0.017) 0.774 (0.017)
DGM3 (c-gumb) 0.732 (0.02) 0.731 (0.02) 0.731 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02)
DGM4 (c-frank) 0.759 (0.018) 0.758 (0.018) 0.759 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018)
DGM5 (f-norm) 0.746 (0.017) 0.745 (0.017) 0.745 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017)
DGM6 (f-gam) 0.771 (0.018) 0.771 (0.018) 0.771 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018)

Table S4.13: Harrel's C-statistic (mean (sd)) for scenario L

n = 1000 n = 2500 n = 5000
DGM1 (msm) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM2 (c-clay) 0.783 (0.074) 0.788 (0.069) 0.786 (0.066)
DGM3 (c-gumb) 0.779 (0.077) 0.788 (0.069) 0.786 (0.066)
DGM4 (c-frank) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM5 (f-norm) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM6 (f-gam) 0.792 (0.067) 0.79 (0.069) 0.787 (0.066)
NA 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
NA 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)

Table S4.14: Harrel's C-statistic (mean (sd)) for scenario H

n = 1000 n = 2500 n = 5000
DGM1 (msm) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM2 (c-clay) 0.809 (0.02) 0.809 (0.021) 0.809 (0.019)
DGM3 (c-gumb) 0.809 (0.02) 0.809 (0.021) 0.809 (0.019)
DGM4 (c-frank) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM5 (f-norm) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM6 (f-gam) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
NA 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
NA 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)

Section 5. Simulation: event rates

Table S5.1: Mean (sd) of the number of uncensored events for outcome A across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 94 (9) 94 (9) 94 (9) 94 (9) 94 (9) 94 (9)
LL 94 (9) 94 (9) 94 (9) 94 (9) 95 (9) 94 (10)
LH 93 (10) 94 (9) 94 (9) 94 (9) 96 (9) 96 (9)
HN 285 (14) 285 (14) 285 (14) 285 (14) 285 (14) 285 (14)
HL 281 (14) 285 (14) 285 (14) 285 (14) 286 (15) 287 (14)
HH 280 (15) 285 (14) 285 (15) 285 (14) 291 (14) 288 (15)

Table S5.2: Mean (sd) of the number of uncensored events for outcome B across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 95 (9) 95 (9) 95 (9) 95 (9) 95 (9) 95 (9)
LL 95 (9) 95 (9) 95 (10) 95 (9) 97 (9) 95 (9)
LH 94 (9) 95 (9) 95 (10) 95 (9) 97 (9) 96 (9)
HN 288 (14) 288 (14) 288 (14) 288 (14) 288 (14) 288 (14)
HL 289 (15) 288 (14) 287 (15) 288 (14) 289 (14) 289 (14)
HH 286 (14) 288 (14) 288 (15) 287 (14) 292 (14) 292 (14)

Table S5.3: Mean (sd) of the number of uncensored events for outcome AB across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 12 (3) 12 (3) 12 (3) 12 (3) 12 (3) 12 (3)
LL 14 (4) 14 (4) 14 (4) 14 (4) 14 (4) 14 (4)
LH 17 (4) 17 (4) 17 (4) 17 (4) 18 (4) 18 (4)
HN 105 (10) 105 (10) 105 (10) 105 (10) 105 (10) 105 (10)
HL 126 (10) 126 (10) 127 (11) 126 (10) 129 (11) 127 (10)
HH 156 (11) 158 (11) 160 (12) 158 (11) 159 (12) 157 (12)

Section 6: Clinical example supplementary figures and tables

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Table S6.1: Baseline data for development and validation cohorts

  development validation Overall
(N=100000) (N=100000) (N=200000)
Age
  Mean (SD) 69.3 (± 5.75) 69.3 (± 5.73) 69.3 (± 5.74)
gender
  0 47089 (47.1%) 47628 (47.6%) 94717 (47.4%)
  1 52911 (52.9%) 52372 (52.4%) 105283 (52.6%)
BMI
  Mean (SD) 27.3 (± 5.25) 27.3 (± 5.26) 27.3 (± 5.26)
Cholesterol/HDL ratio
  Mean (SD) 3.79 (± 1.17) 3.79 (± 1.17) 3.79 (± 1.17)
Ethnicity
  White 93319 (93.3%) 93456 (93.5%) 186775 (93.4%)
  Mixed race 450 (0.450%) 419 (0.419%) 869 (0.435%)
  South asian 3423 (3.42%) 3257 (3.26%) 6680 (3.34%)
  Black 2087 (2.09%) 2157 (2.16%) 4244 (2.12%)
  Chinese and other 721 (0.721%) 711 (0.711%) 1432 (0.716%)
  Other 0 (0%) 0 (0%) 0 (0%)
SBP
  Mean (SD) 139 (± 17.8) 139 (± 17.8) 139 (± 17.8)
Smoking status
  Never 36098 (36.1%) 35933 (35.9%) 72031 (36.0%)
  Ex 35854 (35.9%) 35852 (35.9%) 71706 (35.9%)
  Current 28048 (28.0%) 28215 (28.2%) 56263 (28.1%)
IMD
  1 (most deprived) 24786 (24.8%) 24654 (24.7%) 49440 (24.7%)
  2 22587 (22.6%) 22277 (22.3%) 44864 (22.4%)
  3 20095 (20.1%) 20408 (20.4%) 40503 (20.3%)
  4 17587 (17.6%) 17295 (17.3%) 34882 (17.4%)
  5 (least deprived) 14945 (14.9%) 15366 (15.4%) 30311 (15.2%)

Table S6.2: Outcome data for development and validation cohorts

development validation
Diab_t2.n.at.risk 89211.00 89236.00
Diab_t2.time.at.risk 248673105.00 248217658.00
Diab_t2.number.events 7441.00 7512.00
Diab_t2.rate 10.93 11.05
HF.n.at.risk 97219.00 97225.00
HF.time.at.risk 275713488.00 275489603.00
HF.number.events 6597.00 6450.00
HF.rate 8.74 8.55
CHD_MI.n.at.risk 89008.00 88974.00
CHD_MI.time.at.risk 242660815.00 242941571.00
CHD_MI.number.events 8324.00 8203.00
CHD_MI.rate 12.53 12.33
Stroke_TIA.n.at.risk 94845.00 94736.00
Stroke_TIA.time.at.risk 266075602.00 265233191.00
Stroke_TIA.number.events 7362.00 7478.00
Stroke_TIA.rate 10.11 10.30

Figure S6.1: Graphical calibration curves for each method in the clinical example over the entire range of predicted risk

Figure S6.2: Observed vs predicted risk by decile of predicted risk for each method in the clinical example